6 citations · 18 across the 13 of their papers we have counts for
13 papers
Notes on Hilbert's 16th: experiencing Viro's theory
Alexandre Gabard
This text is intended to become in the long run Chapter 3 of our long saga dedicated to Riemann, Ahlfors and Rohlin. Yet, as its contents evolved as mostly independent (due to our…
A little scholium on Hilbert-Rohn via the total reality of -curves: Riemann's flirt with Miss Ragsdale
Alexandre Gabard
This note presents an elementary proof of Hilbert's 1891 Ansatz of nesting for -sextics, along the line of Riemann's Nachlass 1857 and a simple Harnack-style argument (1876). Ou…
Foliations on non-metrisable manifolds II: contrasted behaviours
Mathieu Baillif, Alexandre Gabard, David Gauld
This paper, which is an outgrowth of a previous paper of the authors, continues the study of dimension 1 foliations on non-metrisable manifolds emphasising some anomalous behaviour…
Ahlfors circle maps and total reality: from Riemann to Rohlin
Alexandre Gabard
This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps…
Euler-Poincaré obstruction for pretzels with long tentacles à la Cantor-Nyikos
Alexandre Gabard
We present an avatar of the Euler obstruction to foliated structures on certain non-metric surfaces. This adumbrates (at least for the simplest 2D-configurations) that the standard…
Ebullition in foliated surfaces versus gravitational clumping
Alexandre Gabard
For surfaces, we brush a reasonably sharp picture of the influence of the fundamental group upon the complexity of foliated-dynamics. A metaphor emerges with phase-changes through…